Would either \(Q_r\)  or \(Q_s\)  not commute with \(H\) , the result of the commutator were bilocal.
This subtlety arises in the case of open boundaries where the parity-odd charges are typically not conserved but still required to generate the full space of admissible deformations [1]}, see Section REF . Note that the charges \(Q_r\)  can be taken to be the spacetime \(P\) - or \(H\) -type charges described in Section REF  or some internal commuting charge, see [2]} for an example of latter. While the \(T\bar{T}\) -deformation belongs to the class of deformations induced by bilocal spacetime charges, the combination of spacetime and internal charge is referred to as \(J\bar{T}\) -deformations in the field theory context,
see [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. Similar deformation for spin chains were considered in [2]}.
